Compactness in Infinitary Godel Logics

摘要

We outline some model-building procedures for infinitary Godel logics, including a suitable ultrapower construction. As an application, we provide two proofs of the fact that the usual characterizations of cardinals k such that the Compactness and Weak Compactness Theorems hold for the infinitary language L_(κ,κ) are also valid for the corresponding Godel logics.